Physics of 2d object collisions using f=ma???

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Malice... not really...

If the collision is elastic, both momentum and KE is conserved.

If the collision is inelastic, momentum is conserved whilst KE is not.

In other words, momentum is always conserved, KE is sometimes conserved.

I assume though that in a game-world you'll have all collisions be elastic. Therefore it'll be easy to calculate the resultant velocities as both KE and momentum is conserved.